A method for tracking the navigation of a mobile carrier, in which an extended Kalman filter estimates, over successive iterations, a navigation state of the carrier. Each iteration propagates a previous navigation state of the carrier into a propagated state, updates the propagated state according to measurements acquired by at least one navigation sensor. The updating includes: calculating a linear correction term from an innovation representative of a difference between the measurements acquired by the navigation sensor and the propagated state, calculating an exponential of the linear correction in terms of a Lie group, calculating a first correction term expressed in a reference frame that is fixed relative to the carrier, calculating a second correction term expressed in an inertial reference frame in which the carrier is mobile, and adding the second correction term to the value of the variable contained in the propagated state.